1
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Chen G, Zhang H, Lu T, Jiang Y. The stress deformation response influenced by the chain rigidity for mesostructures in diblock copolymers. Phys Chem Chem Phys 2021; 23:22992-23004. [PMID: 34611676 DOI: 10.1039/d1cp03159g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A self-consistent field theory formalism based on the wormlike chain model is developed to investigate the stress-strain relation for mesostructures in diblock copolymers under the influence of chain rigidity, involving the adjustable simulation cell in the non-orthogonal coordinates by means of optimization of free energy. We elucidate the effect of the chain persistency broadly spanning from the Gaussian chain to the rigid rodlike chain on the elastic response of mesophases that deviate from the initial equilibrium structures. We analytically and numerically demonstrate that our current approach in the long chain limit recovers to the Gaussian-chain-based theory. Being ascribed to the distinct conformational behaviors for flexible chains and rigid rodlike chains, the tensile and compressive stresses applied to lamellae exhibit asymmetric deformation behaviors and the shear stress applied to the initial equilibrium hexagonal cylinders results in noticeable deviations in the shape and spatial arrangement of cylindroids for various chain rigidity values. For the zero stress, in addition, our approach can be straightforwardly utilized to explore the optimal size and shape of the simulation cell in order to achieve a stress free configuration of systems.
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Affiliation(s)
- Gaohang Chen
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Hui Zhang
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
| | - Teng Lu
- Computer Network Information Center of the Chinese Academy of Sciences, Beijing 100190, China
| | - Ying Jiang
- School of Chemistry and Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China. .,Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
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2
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Friedowitz S, Qin J. Reversible ion binding for polyelectrolytes with adaptive conformations. AIChE J 2021. [DOI: 10.1002/aic.17426] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Sean Friedowitz
- Department of Chemical Engineering Stanford University Stanford California USA
| | - Jian Qin
- Department of Chemical Engineering Stanford University Stanford California USA
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3
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Huang J, Li S, Zhang X, Huang G. Neural network model for structure factor of polymer systems. J Chem Phys 2020; 153:124902. [PMID: 33003754 DOI: 10.1063/5.0022464] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
As an important physical quantity to understand the internal structure of polymer chains, the structure factor is being studied both in theory and experiment. Theoretically, the structure factor of Gaussian chains has been solved analytically, but for wormlike chains, numerical approaches are often used, such as Monte Carlo simulations, solving the modified diffusion equation. In these works, the structure factor needs to be calculated differently for different regions of the wave vector and chain rigidity, and some calculation processes are resource consuming. In this work, by training a deep neural network, we obtained an efficient model to calculate the structure factor of polymer chains, without considering different regions of wavenumber and chain rigidity. Furthermore, based on the trained neural network model, we predicted the contour and Kuhn lengths of some polymer chains by using scattering experimental data, and we found that our model can get pretty reasonable predictions. This work provides a method to obtain the structure factor for polymer chains, which is as good as previous and more computationally efficient. It also provides a potential way for the experimental researchers to measure the contour and Kuhn lengths of polymer chains.
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Affiliation(s)
- Jie Huang
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Shiben Li
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Gang Huang
- Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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4
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Chen Y, Zhang X, Jiang Y. The influence of side-chain conformations on the phase behavior of bottlebrush block polymers. SOFT MATTER 2020; 16:8047-8056. [PMID: 32785406 DOI: 10.1039/d0sm00918k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A self-consistent field theory based on the wormlike chain model is implemented in the investigation of the self-assembly behavior of bottlebrush block polymers in the formation of a lamellar phase. We utilize the model in which the semi-flexible side chains of two types A and B are grafted at the semi-flexible backbone of type C to mimic the bottlebrush molecule, particularly allowing for the extended chain conformation due to the high grafting density. We examine the positional and orientational probability distribution for the segments along the backbone and side chains as a function of the grafting density and chain flexibility for all blocks, covering a broad regime spanning from the flexible chain to rigid rod chain. This reveals that the persistence length of side chains λSC which intrinsically tunes the chain conformation of bottlebrush polymers plays a pivotal role in determining the manner of the local monomer packing in microphase segregation. As an important adjustable factor, λSC has a remarkable impact on the backbone extension and then realizes the effective manipulation of the characteristic structural size of self-assembled microstructures, such as the domain spacing and the interfacial width.
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Affiliation(s)
- Yuguo Chen
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.
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5
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Osipov MA, Gorkunov MV, Antonov AA. Density Functional Approach to the Molecular Theory of Rod-Coil Diblock Copolymers. POLYMER SCIENCE SERIES A 2020. [DOI: 10.1134/s0965545x20050132] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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6
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Osipov MA, Gorkunov MV, Antonov AA. Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers. Polymers (Basel) 2020; 12:polym12061262. [PMID: 32486492 PMCID: PMC7361701 DOI: 10.3390/polym12061262] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Revised: 05/26/2020] [Accepted: 05/27/2020] [Indexed: 11/16/2022] Open
Abstract
Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.
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Affiliation(s)
- Mikhail A. Osipov
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, Scotland, UK
- Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 119991 Moscow, Russia
- Correspondence:
| | - Maxim V. Gorkunov
- Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics“, Russian Academy of Sciences, 119333 Moscow, Russia; (M.V.G.); (A.A.A.)
| | - Alexander A. Antonov
- Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics“, Russian Academy of Sciences, 119333 Moscow, Russia; (M.V.G.); (A.A.A.)
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7
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Chen X, Qi S, Zhang X, Yan D. Influence of Small-Scale Correlation on the Interface Evolution of Semiflexible Homopolymer Blends. ACS OMEGA 2020; 5:7593-7600. [PMID: 32280903 PMCID: PMC7144130 DOI: 10.1021/acsomega.0c00421] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
Within the framework of a dynamic self-consistent field theory, we study the effect of the correlations in a small scale on polymer dynamics, adopting the semiflexible homopolymer blends as the model system. This is accomplished by taking the pair correlation function of ideal semiflexible chains as the Onsager coefficient and the Debye function as an approximation to the Onsager coefficient. Relying on the difference of the two pair correlation functions in the small-scale region, we can identify the effect of small-scale correlations. In the equilibrium state, with the chain length growing, the interface width has a continuous transition from the contour length to radius of gyration. The investigation of interfacial evolution and chain orientation reveals that strong small-scale correlations would accelerate the small-scale dynamic process. We also expect that such a small-scale effect should be highlighted in the process where microscopic phase separation happens.
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Affiliation(s)
- Xinxiang Chen
- Department
of Physics, Beijing Normal University, Beijing 100875, China
| | - Shuanhu Qi
- School
of Chemistry, Beihang University, Beijing 100191, China
| | - Xinghua Zhang
- School
of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Dadong Yan
- Department
of Physics, Beijing Normal University, Beijing 100875, China
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8
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Zhang J, Kremer K, Michels JJ, Daoulas KC. Exploring Disordered Morphologies of Blends and Block Copolymers for Light-Emitting Diodes with Mesoscopic Simulations. Macromolecules 2020; 53:523-538. [PMID: 32655190 PMCID: PMC7343280 DOI: 10.1021/acs.macromol.9b02402] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Revised: 12/20/2019] [Indexed: 01/29/2023]
Abstract
![]()
Recently,
disordered blends of semiconducting and insulating polymers have been
used to prepare light-emitting diodes with increased luminous efficiency.
Because the thermodynamic stability of the disordered phase in blends
is limited, equivalent diblock copolymers (BCPs) could be an alternative.
However, the choice between disordered blends and BCPs requires understanding
structural differences and their effect on charge carrier transport.
Using a hybrid mesoscopic model, we simulate blends and equivalent
BCPs of two representative semiconducting and insulating polymers:
poly(p-phenylene vinylene) (PPV) and polyacrylate.
The immiscibility is varied to mimic annealing at different temperatures.
We find stable or metastable disordered morphologies until we reach
the mean-field (MF) spinodal. Disordered morphologies are heterogeneous
because of thermal fluctuations and local segregation. Near the MF
spinodal, segregation is stronger in BCPs than in the blends, even
though the immiscibility, normalized by the MF spinodal, is the same.
We link the spatial distribution of PPV with electric conductance.
We predict that the immiscibility (temperature at which the layer
is annealed) affects electrical percolation much stronger in BCPs
than in blends. Differences in the local structure and percolation
between blends and BCPs are enhanced at a high insulator content.
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Affiliation(s)
- Jianrui Zhang
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Kurt Kremer
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Jasper J Michels
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Kostas Ch Daoulas
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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9
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Hou R, Wang N, Bao W, Wang Z. Polymer-Based Accurate Positioning: An Exact Worm-like-Chain Study. ACS OMEGA 2018; 3:14318-14326. [PMID: 31458122 PMCID: PMC6644801 DOI: 10.1021/acsomega.8b01448] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/26/2018] [Accepted: 10/18/2018] [Indexed: 06/10/2023]
Abstract
Precise positioning of molecular objects from one location to another is important for nanomanipulation and is also involved in molecular motors. Here, we study single-polymer-based positioning on the basis of the exact solution to the realistic three-dimensional worm-like-chain (WLC) model. The results suggest the possibility of a surprisingly accurate flyfishing-like positioning in which tilting one end of a flexible short polymer enables positioning of the other diffusing end to a distant location within an error of ∼1 nm. This offers a new mechanism for designing molecular positioning devices. The flyfishing effect (and reverse process) likely plays a role in biological molecular motors and may be used to improve speed of artificial counterparts. To facilitate these applications, a new force-extension formula is obtained from the exact WLC solution. This formula has an improved accuracy over the widely used Marko-Siggia formula for stretched polymers and is valid for compressed polymers too. The new formula is useful in analysis of single-molecule stretching experiments and in estimating intramolecular forces of molecular motors, especially those involving both stretched and compressed polymer components.
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Affiliation(s)
- Ruizheng Hou
- Department
of Applied Physics, School of Science, and Institute of Quantum Optics
and Quantum Information, Xi’an Jiaotong
University, Xi’an, Shaan Xi 710049, China
| | - Nan Wang
- Department of Mathematics and NUS Graduate
School for Integrative Sciences
and Engineering, National University of
Singapore, 119076, Singapore
| | - Weizhu Bao
- Department of Mathematics and NUS Graduate
School for Integrative Sciences
and Engineering, National University of
Singapore, 119076, Singapore
| | - Zhisong Wang
- Department of Mathematics and NUS Graduate
School for Integrative Sciences
and Engineering, National University of
Singapore, 119076, Singapore
- Department
of Physics, National University of Singapore, 117542, Singapore
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10
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Mao S, MacPherson Q, Spakowitz AJ. Fluctuation Effects in Semiflexible Diblock Copolymers. ACS Macro Lett 2018; 7:59-64. [PMID: 35610917 DOI: 10.1021/acsmacrolett.7b00638] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a simulation study of the equilibrium thermodynamic behavior of semiflexible diblock copolymer melts. Using discretized wormlike chains and field-theoretic Monte Carlo, we find that concentration fluctuations play a critical role in controlling phase transitions of semiflexible diblock copolymers. Polymer flexibility and aspect ratio control the order-disorder transition Flory-Huggins parameter χODTN. For polymers with low aspect ratios, fluctuations strongly elevate the phase transition χODTN at finite molecular weights. For high aspect-ratio polymers, chain semiflexibility decreases the phase transition χODTN. We find that the simulated phase behavior agrees well with our recently developed fluctuation theory based on wormlike chain configurations and a one-loop treatment of concentration fluctuations.
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Affiliation(s)
- Shifan Mao
- Department of Chemical Engineering, ‡Department of Physics, §Department of Materials Science and
Engineering, ∥Department of Applied Physics, and ⊥Biophysics Program, Stanford University, Stanford, California 94305, United States
| | - Quinn MacPherson
- Department of Chemical Engineering, ‡Department of Physics, §Department of Materials Science and
Engineering, ∥Department of Applied Physics, and ⊥Biophysics Program, Stanford University, Stanford, California 94305, United States
| | - Andrew J. Spakowitz
- Department of Chemical Engineering, ‡Department of Physics, §Department of Materials Science and
Engineering, ∥Department of Applied Physics, and ⊥Biophysics Program, Stanford University, Stanford, California 94305, United States
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11
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Jiang Y, Li S, Chen JZY. Perspective: parameters in a self-consistent field theory of multicomponent wormlike-copolymer melts. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:91. [PMID: 27696016 DOI: 10.1140/epje/i2016-16091-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2016] [Accepted: 09/13/2016] [Indexed: 06/06/2023]
Abstract
We review a formalism that can be used to calculate the microphase-separated crystallographic structures of multi-component wormlike polymer melts. The approach is based on a self-consistent field theory of wormlike polymers where the persistence length of each component is an important parameter. We emphasize on an analysis of the number of independent parameters required to specify a problem in general, for a system that includes Flory-Huggins and Maier-Saupe energies. Examples of recent applications are also briefly demonstrated: AB homopolymer interface, AB diblock copolymers, and rod-coil copolymers.
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Affiliation(s)
- Ying Jiang
- School of Chemistry and Environment, Center of Soft Matter Physics and its Applications, Beihang University, 100191, Beijing, China
| | - Shiben Li
- Department of Physics, Wenzhou University, 325035, Wenzhou, Zhejiang, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada.
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12
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Bu X, Zhang X. Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers. Polymers (Basel) 2016; 8:E301. [PMID: 30974614 PMCID: PMC6432401 DOI: 10.3390/polym8090301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Revised: 08/05/2016] [Accepted: 08/08/2016] [Indexed: 11/16/2022] Open
Abstract
The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory.
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Affiliation(s)
- Xiangyu Bu
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
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13
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14
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Jiang Y, Zhang X, Miao B, Yan D, Chen JZY. Microphase separation of short wormlike diblock copolymers with a finite interaction range. SOFT MATTER 2016; 12:2481-2490. [PMID: 26822622 DOI: 10.1039/c5sm02865e] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We investigate several structural properties of low-molecular weight AB diblock copolymer melts, focusing on a number of features that substantially deviate from those of high-molecular weight copolymer melts. The study is based on the wormlike chain formalism aided by random phase approximation and self-consistent field theory. We examine the effects that stemmed from both the finite molecular weight and the finite interaction range between unlike AB monomers. The latter yields profound effects on systems consisting of short wormlike block copolymers. The noticeable shift of the order-disorder transition point is discussed. Attention is also paid to the strong-segregation regime, where low molecular weight polymers are subject to finite stretchability.
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Affiliation(s)
- Ying Jiang
- School of Chemistry and Environment, Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China.
| | - Bing Miao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China.
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Jeff Z Y Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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15
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Tang J, Jiang Y, Zhang X, Yan D, Chen JZY. Phase Diagram of Rod–Coil Diblock Copolymer Melts. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b02235] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Jiuzhou Tang
- Beijing
National Laboratory For Molecular Sciences (BNLMS), Laboratory of
Polymer Physics and Chemistry, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Ying Jiang
- School
of Chemistry and Environment, Beihang University, Beijing 100083, China
| | - Xinghua Zhang
- School
of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Dadong Yan
- Department
of Physics, Beijing Normal University, Beijing 100875, China
| | - Jeff Z. Y. Chen
- Department
of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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16
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Tang J, Zhang X, Yan D. Compression induced phase transition of nematic brush: A mean-field theory study. J Chem Phys 2015; 143:204903. [PMID: 26627971 DOI: 10.1063/1.4936324] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.
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Affiliation(s)
- Jiuzhou Tang
- Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
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17
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Liao Y, Miao B. Structure factor of a Gaussian chain confined between two parallel plates. J Chem Phys 2015; 142:164903. [DOI: 10.1063/1.4919305] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yi Liao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Bing Miao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
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18
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Jiang Y, Zhang X, Miao B, Yan D. The study of the structure factor of a wormlike chain in an orientational external field. J Chem Phys 2015; 142:154901. [PMID: 25903904 DOI: 10.1063/1.4917520] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ying Jiang
- School of Chemistry and Environment, Center of Soft Matter Physics and its Applications, Beihang University, Beijing 100191, China
| | - Xinghua Zhang
- School of Science, Beijing Jiaotong University, Beijing 100044, China
| | - Bing Miao
- College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dadong Yan
- Department of Physics, Beijing Normal University, Beijing 100875, China
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19
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Li S, Jiang Y, Chen JZY. Phase transitions in semiflexible-rod diblock copolymers: a self-consistent field theory. SOFT MATTER 2014; 10:8932-8944. [PMID: 25299162 DOI: 10.1039/c4sm01884b] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate the phase behavior of semiflexible-rod diblock copolymers in a parameter range where the system displays columnar and lamella structures, using a self-consistent field theory based on the wormlike-chain model. Both Flory-Huggins and Maier-Saupe orientational interactions are incorporated in the formalism, which allows us to explore microphase separation and liquid-crystal ordering simultaneously. Order-to-order phase transitions induced by chain rigidity and orientational interaction are both reported and analyzed. Coupled orientational ordering and spatial inhomogeneity of the four microphase-separated states are discussed in this work: hexagonal column, ellipse column, smectic-A, and smectic-C.
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Affiliation(s)
- Shiben Li
- Department of Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China
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